A map slope measuring tool

I've developed a script to create a map contour slope measuring tool.  Like my Clone and windshield scripts, it uses parameters to allow the user to tailor it to their needs, and it's also written in PostScript.

The following factors can be set:

map scale
map vertical contour spacing
number of contours between 'index' (thicker) contour
number of index 'series'
minimum slope angle
maximum slope angle
physical size of the tool

The tool draws a number of series of contour lines, which widen according to the slope angle scale.  To measure the slope from the map, place to tool over the map slope in question, and move the tool until you find the point where the tool contours match the map contours, and read the slope angle (or 1 in x value) off the scales.

Once you've set the parameters to suit your needs, simply print the tool onto a transparency, ideally in a laser printer.  The script will print an array of tools on a single transparency, saving waste.  I suppose I could get it to print a series of different scales, making it more use to a single user...

Since the script calculates all values and draws the contour lines mathematically, the tool should be perfect (barring printer scaling errors).  And, since you can enter any scale you want, you can create a tool for OS 1:25k (5m or 10m contour), 1:50k, 1:63360, Harvey's 1:40k (15m), or whatever other bizarre scale you find.  The map scale and contour spacing are printed on the tool, to avoid confusion.

The idea came about as a result of my reading on navigation, having decided I probably need to teach 'accepted practice' in DofE, rather than my self-taught methods.  Having found the 'Keayscale' in Wally Keay's DofE Navigation book, I looked at his contour measurement scales, which have gaps between black blocks, where the gap is the size of n contour spacings, for a given slope angle.  I thought that, rather than simply quote the number of lines that should fit in the gap, I'd draw the lines in the gap.  And, rather than put the scale along the edge of a piece of card, they could be printed on a transparency to overlay on the map.  It was a simple progression to a set of continuously varying slope contours used in the tool.

Here's a rather low-resolution image of an example tool: [rats, OM image insert broken again..]

Any interest?  Any thoughts?  Is it an old idea that I've re-invented?

Finally managed to get the image to insert...

No, sorry, didn't get any of that, Cap. What does it do?

I understand about aspect of the slope - am I getting warm?

Three initial thoughts...

1. Neat idea

2. I'm guessing it's easier to use on relatively uniform slopes rather than intricate areas full of wiggling contours? 

3. If I understood your parameter list it would be possible to produce one covering a steeper range of slopes (possibly at the expense of the shallower range)? I'm thinking of something covering the crucial 30 to 45 degree zone for avalanche risk.

I agree with MattC, it's a neat idea. However, what practical uses does it have? Obviously the avalanche risk is a good application. However, for almost all other purposes I can just glance at the map and mentally grade the slope on my "Easy stroll" to "Mega-slog" scale. I wouldn't really be interested in the actual mathematical aspect.

I agree again, as a walker / scrambler I can't see that it would make much difference - looking at the map is enough to visualise approximate difficulty, and any walker not able to read a map to that extent is unlikely to seek out a tool.

??more useful to Mountain Bikers where angle might be more important?

??DOE / school / other group expeditions where written health and safety audits are needed

Ah, on a large screen and not late at night, I see what it does.

In real life, slopes are rarely uniform for any distance.  Surely you'd end up having to individually measure sections of an actual slope and piece them together to get a complete idea of the total climb / descent?

It feels a bit too fiddly for practical use - a bit like Tranter's variations to Naismith's rule - but I can see how it could be useful where accuracy of slope is critical - avalanches or cheese-rolling contests.

Having printed one onto transparency, and had a play with it, it works okay at moderate angles, but gets a bit fussy at the steeper angles. I could easily modify it to only display the index contours beyond a certain minimum contour spacing (much as the OS do).

You don't have to find a whole series of contours that are at the same slope; you can measure the slope defined by any two adjacent contours, at any point on the wiggly lines, provided you align the tool so that the 'read-off' lines are roughly perpendicular to the map contours.

At the low angle end, where the 'trumpet' opens up, the scale contours are diverging rapidly, so you can't align the lines; you have to compare the gaps between the lines. This is what you do throughout the scale, just it's not quite as obvious.

And yes, Matt, you can specify whatever narrow angle range you're interested in, and what angle values are displayed along the scales axis.

As for the point of it, I'm not convinced either; I've never used such a tool in the past, but having seen another tool to do this (the Keayscale), I thought I saw a way to make a better tool... Also, Lyle Brotherton's 'Ultimate Navigation Manual' discusses the concept of foreshortening, and another version of the tool will allow you to read the additional 'along the slope' distance over the horizontal distance. I' m not convinced that this technique has any merit in practice, since the additional distance is only 3% even at a 1 in 4 slope, and my stride length is significantly changed at that sort of slope, so any changes to pacing counts will be dominated by the stride length change, rather than the additional sloping distance.

Anyway, if anyone wants the PostScript to have a play, drop me a PM with an email address.

Well, I added the ability to not display non-index contours below a specified line spacing, and the ability to plot a series of tools for different map scales.  Whilst it works in metres, you can specify the map contour spacing as an abritrary unit, provided you give a metric scale factor.  So you can draw a tool for a 50ft OS Series 7 one-mile, 1:63360 map if you should wish...

I'm not sure if the continuous curve is useful, and I may revert to the original plan which was to have discrete, stepped lines (basically, moving the measurements from the edge of a card to within the body of a transparent tool).  The opaque card version may actually work better, as it hides the confusing map contours, and allows you to concentrate on comparing just the map contours and the scale.

maybe you could try this as some type of polar plot. Then you've got a graphical representation of the slope was well.

Well, that's an interesting variation; I'm having a play with the idea. It's a bit compressed at the moment

Guess it might have to look like one of your cone templates. No need for the origin.

Looks similar to the tool used to estimate geostrophic wind speed from isobar spacing...which thinking about it is not that suprising.